Semantics is really messy especially when dealing with statistics. Ditto on Bob Shannon's references and also you may want to look at papers published by Mark A. Tries of University of MA Lowell (sometimes et. al.) who has authored a number of good papers on counting statistics.
If you use zero you most likely are adding a bias to your conclusions. This bias may be high or low. ISO 11929 2008 and the below references Bob submitted are in agreement that zero is not an appropriate approximation of the value if less than the detection limit. A bias may create problems is conclusions are incorrect as a result of the bias. Unbiased data should be used for all calculations performed to provide a best estimate for reporting based on an acceptable percentage of false + and false - results. Even if reporting a best estimate it is often useful to report or at least maintain a record of the actual measurements and errors on the measurements.
I have never seen value/2, perhaps the person who started that was confusing the 95% MDA with the Lc (detection limit) and taking half of the MDA or 1/2 x 4.66sigma.
Hope this helps.
Barbara Reider, CHP
-----Original Message-----
From: Arvic Harms <Arvic.Harms at npl.co.uk>
To: Bob Shannon <BobShannon at earthlink.net>; radsafe at radlab.nl
Cc: Peter Bossew <Peter.Bossew at reflex.at>
Sent: Mon, Oct 5, 2009 7:23 am
Subject: RE: [ RadSafe ] Comparison of a Measured Resultto the Critical/Decision Level; ne
w question
Dear all,
ISO 11929 2008 draft has the following recommendations in Chapter 6:
If result < y* (decision threshold), report as 'not detected' or alternatively
s 'less than y# (detection limit)', if required by a regulator.
f result >= y*, report the best estimate of the result together with its
ncertainty (even if the result is less than y#, the detection limit).
I have a question about combining results which contain one or more 'less than
#' types of "results" when you want, for instance, to calculate a mean of
everal results.
It is common to assign a value of [y# divided by factor of 2] to the 'less than
#' results. Is there any scientific justification for doing this?
The 'less than y#' types of "results" are 'not detected' and are therefore 0 and
ot y# / 2 in my opinion.
Kind regards,
Arvic Harms
r Arvic Harms
ational Physical Laboratory
ampton Road
eddington TW11 0LW
iddlesex
nited Kingdom
-mail: arvic.harms at npl.co.uk
el ++44 20 8943 8512
ax ++44 20 8614 0488
> -----Original Message-----
From: radsafe-bounces at radlab.nl [mailto:radsafe-bounces at radlab.nl]On
Behalf Of Bob Shannon
Sent: 04 March 2009 20:38
To: radsafe at radlab.nl
Cc: 'Peter Bossew'
Subject: RE: [ RadSafe ] Comparison of a Measured Resultto the
Critical/Decision Level
Peter -
I very much agree with the main thrust of your comment about critical
levels. Thanks!
I have some concerns about censoring measurement results as you have
proposed, though.
Most standards that apply to radiochemical
measurements
(at least in the US) specify that every measured result,
whether positive,
negative or zero, should be reported in association with its
measurement
uncertainty. While there are a few programs that make
exceptions, and some
entities fail to follow the guidance, but the guidance is presented in
rather unambiguous terms. Here are several examples:
· Multi-Agency Radiological Laboratory Analytical
Protocols Manual
(MARLAP) - EPA, NRC, DOE, DOD, DHS, FDA, USGS, NIST (NUREG-1576, EPA
402-B-04-001A, NTIS PB2004-105421).
o Section 19.3.8 Reporting the Measurement Uncertainty
§ It is possible to calculate radioanalytical results that
are less than
zero, although negative radioactivity is physically
impossible. Laboratories
sometimes choose not to report negative results or results
that are near
zero. Such censoring of results is not recommended. All
results, whether
positive, negative, or zero, should be reported as obtained,
together with
their uncertainties.
· ANSI N13.30 - Performance Criteria for Radiobioassay, Health
Physics Society N13.30-1996
o 3.5 Reporting Results [results reported shall include]
(5) quantification of the amount of radionuclide(s) (whether positive,
negative, or zero) of each radionuclide measured in each part
of the body
counted;
(6) estimates of counting uncertainty
and the total
propagated uncertainty
[which includes counting and other random and systematic
uncertainties at
one sigma (see Appendix D, Section D.6)];
(7) value of the decision level and a priori MDA, in units
consistent with
the results;
· ANSI N42.23 American National Standard Measurement
and Associated
Instrument Quality Assurance for Radioassay Laboratories,
(IEEE, 1996/2004)
o A.8 Reporting results by the service laboratory
§ "Calculated concentration or activity value (whether
negative, positive,
or zero) using the appropriate blank for each nuclide" [and]
"Estimates of
the counting uncertainty and total propagated uncertainty
(which contains
counting and other random and systematic uncertainties" [must
be included in
the analytical results reported by the service laboratory]
Bob Shannon
Quality Radioanalytical Support, LLC
BobShannon at earthlink.net
Tel: 303-432-1137
-----Original Message-----
From: radsafe-bounces at radlab.nl
[mailto:radsafe-bounces at radlab.nl] On Behalf
Of Peter Bossew
Sent: Wednesday, March 04, 2009 7:44 AM
To: Redmond, Randy (RXQ); <radsafe at radlab.nl>
Subject: Re: [ RadSafe ] Comparison of a Measured Result to the
Critical/Decision Level
Randy,
the "error" (more accurately: uncertainty) is irrelevant for this. The
"result" (estimate of expectation of a rnd. variable) has to
be compared
to the decision level or threshold. If, like in your case,
result < Lc, it
has to be reported as (quantity) < MDA (also called LLD).
Also the alpha
and beta values connected to Lc and MDA should be reported.
Only if the "result" > Lc, it must be reported together with
uncertainty
(incl. k=number of sigmas), or ideally, with a confidence
interval (again
with k) (because the distribution is not symmetrical, which
is relevant
for low level measurements. This can only be ignored for high
enough count
numbers).
The relevant document is ISO 11929: Determination of the
detection limit
and decision threshold for ionizing radiation measurements. Geneva
2000-2001 (8 parts).
For a good review of theory, De Geer L. (2005): A decent Currie at the
PTS. Report CTBT/PTS/TP/2005-1, Aug. 2005; available from the
CTBTO. Also:
De Geer L. (2004): Currie detection limits in gamma-ray spectroscopy.
Appl. Rad Isot. 61 (2-3), 151-160.
In Bayesian reasoning:
- Weise K. and W. Wöger (1993): A Bayesian theory of measurement
uncertainty. Meas. Sci. Techn. 4(1), 1-11;
- Weise K. et al. (2006): Bayesian decision threshold,
detection limit and
confidence limizs in ionising-radioation measurement. Rad. Prot. Dos.
121(1), 52-63;
- Michel R. (2000): Quality assurance of nuclear analytical techniques
based on Bayesian characteristic limits. J.
Radioanalytical
Nucl. Chem.
245(1), 137-144.
For non-Currie decision rules: Strom and MacLellan (2001):
Evaluation of
eight decision rules for low-level radioactivity counting.
Health Physics
81 (1), 27-34. The authors show that the standard rules (ISO
11929) may
not perform well in extreme cases.
Peter
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